The difference between the selling prices of an item at a profit of 9% and 7% was Rs 190. Find the cost price of the item.

Options

A. Rs, 9,200
B. Rs 9,500
C. Rs 8,700
D. Rs 9,000

Answer

To solve the problem, we need to find the cost price (CP) of the item based on the given selling prices (SP) at different profit percentages.

### Step-by-Step Solution:

1. **Define the Cost Price (CP)**:
Let the cost price of the item be Rs \( x \).

2. **Calculate Selling Price at 9% Profit**:
The selling price when there is a profit of 9% can be calculated as:
\[ SP_{9\%} = CP + 9\% \text{ of } CP = x + \frac{9}{100}x = \frac{109}{100}x \]

3. **Calculate Selling Price at 7% Profit**:
The selling price when there is a profit of 7% can be calculated as:
\[ SP_{7\%} = CP + 7\% \text{ of } CP = x + \frac{7}{100}x = \frac{107}{100}x \]

4. **Find the Difference Between Selling Prices**:
According to the problem, the difference between the selling prices at 9% and 7% profit is Rs 190:
\[ SP_{9\%} - SP_{7\%} = 190 \]
Substituting the expressions for SP:
\[ \frac{109}{100}x - \frac{107}{100}x = 190 \]

5. **Simplify the Equation**:
Combine the fractions:
\[ \frac{109x - 107x}{100} = 190 \]
This simplifies to:
\[ \frac{2x}{100} = 190 \]

6. **Solve for Cost Price (CP)**:
Multiply both sides by 100 to eliminate the fraction:
\[ 2x = 19000 \]
Now, divide both sides by 2:
\[ x = 9500 \]

7. **Conclusion**:
The cost price of the item is Rs 9500.